OK, But Not Great
Until I read Geoff Johns' Action Comics story Superman and the Legion of Super-Heroes, I'd never really understood the appeal of the Legion. In that story, however, Johns was able to tell a tale that had a strong focus on character, allowing readers to get to know each character individually and get a handle on who they were, an incredibly important thing to do when dealing with a team like the Legion that has so many characters. While Johns had his moments in this story, I felt he was unable to duplicate what he had done in his Action Comics story. Legion of 3 Worlds certainly has its moments and its strengths, but I wish Johns had continued to focus on character rather than constantly aim to create one epic moment after another.
To be honest, while this does relate to the main Final Crisis story, there are far more references to Infinite Crisis, also written by Johns, which I'd highly recommend you have read to completely understand this story. Other stories referenced in this one include The Lightning Saga, which was a Justice League/Justice Society crossover, the previously mentioned Superman and the Legion of Superheroes, and surprisingly the massive Green Lantern/Green Lantern Corps crossover The Sinestro Corps War. Of course Johns does his best to explain things so new readers could understand, but some sort of previous knowledge of the Legion would be highly beneficial.
There were a number of things I did like about this story. If you're a fan of big action sequences involving lots of characters, like the ones in the Sinestro Corps War, you'll enjoy this as well. Johns is occasionally able to write some great character moments - one conversation in particular between Polar Boy and Sun Boy was touching, and the interactions between the three main Legion characters - Cosmic Boy, Saturn Girl and Lightning Lad - were enjoyable as well. One scene in particular, where Cosmic Boy loses his temper with Lightning Lad and reminds him about how much he's sacrificed to be the leader of the Legion, was fantastic, and something I thought this story could use more of. Johns also goes for some big moments by (minor spoilers!) bringing back a couple characters who had been previously dead (though I won't say who - you'll have to read it to find out!) and revealing the true identity of the Time Trapper. While I'm generally not a big fan of resurrecting comic book characters, I realize it's become a normal thing, and they were actually both handled fairly well - the first one was the one I was more happy to see back, but the explanation of his return was a little more confusing that the second, which was written simply and rather effectively. The Time Trapper reveal was something else I really enjoyed, I thought it was a cool idea. George Perez is on art for this, and he does a wonderful job of drawing each character, and he clearly put a lot of time and effort into it. Each of the many characters is distinguishable even in big two-page layouts, where some artists tend to draw indistinct figures in backgrounds that all look fairly similar.
Unfortunately, there were also things I didn't like about this story. First and foremost was the return of a character who seems to be well-liked by Johns: Superboy-Prime. Superboy-Prime, in my opinion, is too much of a one-note character to be a truly great villain, built solely on the anger of his world being destroyed, and this story failed to change my mind about that. Some people may like him or feel he's a more complex character than I think he is, but he just doesn't do it for me. Also, this story has a LOT of characters - just look at the character list on this page, you'll see what I mean - and the difficulty of keeping them all straight or remembering what each character was like personality-wise took away from my enjoyment of the story. There was something about the pacing of the story I felt was a little off, as I enjoyed the first, fourth and fifth issues, but for some reason the second and third issues fell kind of flat for me. Usually when I read something by Geoff Johns I find myself reading in large chunks, but I never felt the need to read more than an issue or two at a time with this story. Finally, as much as I enjoyed Perez's art, a lot of the pages felt overly crowded to me, there were a lot of pages with 10 or more panels and it felt like they had way too much going on visually. I'm not sure whether this was because of Perez's style or if it was necessitated by Johns' original script, but it was something I felt could have been improved.
If you're a fan of the Legion of Super-Heroes or Superman-Prime, you'll probably like this story and I would recommend it to you. If you're reading this solely because it has Final Crisis in the title and don't care about the Legion or Superboy-Prime, then this story has only minor implications on the main Final Crisis storyline, so it's up to you if you feel it is necessary to read or not . If you're simply looking for a good comic regardless of which characters are in it or which events it's linked to, then I'd say this story is a decent read, but not a great one or one that needs to be read by all comic book fans. While the story does have its strengths, I don't think this is at the same level of Johns' best work, like his runs on The Flash, Green Lantern and most recently Aquaman.